Design and simulation of a novel dual current mirror based CMOS-MEMS integrated pressure sensor

This paper presents a novel dual current mirror based CMOS circuit for design and development of highly sensitive CMOS-MEMS integrated pressure sensors. The proposed pressure sensing structure has been designed using piezoresistive effect in MOSFETs and 5 μ m standard CMOS technology parameters. The proposed structure includes six p- and n-channel MOSFETs and two square silicon diaphragms. MOSFETs MP1 and MN1 are the reference transistors and are placed on the substrate. The pressure sensing MOSFETs MP2 and MP3 are integrated at the mid of ﬁxed edge and at the centre of the diaphragm-1 to sense the maximum tensile and compressive stress developed due to applied pressure. Sim-ilarly, the pressure sensing MOSFETs MN2 and MN3 are embedded at the mid of ﬁxed edge and at the centre of the diaphragm-2. COMSOL Multiphysics and LTspice softwares are used for the design and simulation of proposed sensor. The sensitivity of proposed sensor is found to be approximately 7.7 mV/kPa for an input pressure ranging from 0– 200 kPa. The output voltage of the sensor has a temperature sensitivity of approximately − 0.2 mV/ ◦ C for an operating temperature ranging from − 50 to 100 ◦ C at 200 kPa. This CMOS circuit

. The arterial blood pressure transmitted via fluid deflects the diaphragm of pressure sensor.
The above mentioned pressure sensor requirement for BP measurement drives researchers to design and develop highly sensitive, compact sized and low cost miniaturized pressure sensors. These sensors work on the principle of deflection of thin flexible diaphragms under externally applied pressure [10]. These deflections are most commonly measured using piezoresistive, capacitive and piezoelectric sensing methods [10][11]. However, each of these methods suffers from inherent limitations [11]. It is important to note that the piezoresistive sensing suffers from temperature cross-sensitivity of silicon piezoresistors and requires temperature compensation circuits [12][13], whereas, capacitive sensing is inherently nonlinear and requires complex electronics [14][15][16]. Moreover, piezoelectric sensing suffers from higher noise levels and degradation of material's piezoelectric properties with increasing temperature [17][18]. In another approach, piezo-MOS sensing, that is piezoresistive effect in MOSFET, has also found a promising application in the monolithic integration of CMOS and MEMS [19][20][21]. Piezo-MOSFETs integrated with microstructures have attracted significant interest among the researchers all over the world [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. In particular, various types of MOSFET based pressure transducers have been studied, designed and developed. Jingjing et al. presented a pressure sensor design using MOS based stress-sensitive operational amplifier [28]. Svensson et al. had proposed a MOSFET based pressure sensor design where the gate of the MOSFET acts as the pressure sensing diaphragm [29]. In another work [30], authors had reported a pressure sensing structure using two piezoresistors and two MOSFETs embedded on a square membrane in a Wheatstone bridge configuration. Jachowicz et al., authors had reported a design, modelling and fabrication of pressuresensitive FET [31]. In a recent work [32], the Gardner and group had presented a pressure sensor design using four p-and n-channel MOSFETs embedded on silicon dioxide diaphragm connected in Wheatstone bridge configuration. In recent past, different from previous approaches, our group had introduced the idea of using current mirror circuits for pressure sensor applications. In our previous works [33][34][35][36], design, simulation and experimental results of resistive loaded n-and p-channel MOSFET based current mirror integrated pressure sensors were presented. The pressure sensitivities of these sensors require further improvement.
In this work, a fully CMOS compatible dual current mirror circuit based pressure sensing structure formed by integrating p-and n-channel MOSFET based current mirror circuits has been proposed and designed using standard 5 μm CMOS technology parameters [37]. In this approach, the proposed dual current mirror design serves as the biasing circuit for providing the necessary gate-to-source biasing voltages for the pressure sensing MOSFETs and simultaneously used as readout circuitry for obtaining the output voltage proportional to the input applied pressure. Thus, the proposed sensor design eliminates the use of extra voltage source or any voltage divider resistive network for biasing. Moreover, the absence of resistors in the proposed pressure sensor makes it completely CMOS compatible. The proposed sensor has resulted in a simple design with high sensitivity, low linearity error and low thermal sensitivity. A comparison of the proposed work with a few relevant literatures has also been presented in Table 1 to highlight the novelty of the proposed design. The work presented in this paper is a step ahead in the design and development of highly-sensitive CMOS-MEMS integrated pressure sensors.
Dual current mirror based CMOS-MEMS integrated pressure sensing structure The proposed dual current mirror based CMOS-MEMS integrated pressure sensing structure integrates a p-MOSFET based current mirror and an n-MOSFET based current mirror circuit as shown in Figure 1. Figure 2 illustrates the cross-sectional view of the proposed CMOS pressure sensor.
The pressure sensing structure consists of two identical square-shaped diaphragms each having a length of 100 μm and a thickness of 2.5 μm. MOSFETs MP1 and MN1 of the dual current mirror based CMOS circuit are the constant current source transistors and act as reference transistors. These transistors are embedded on the silicon substrate. The pressure sensing transis-  sensing MOSFETs will experience tensile and compressive stresses developed in the diaphragms under externally applied pressure and result in the variation of their carrier mobility. This variation in carrier mobility will thus result in the variation of drain currents and voltages of the pressure sensing MOSFETs. Therefore, an output voltage proportional to externally applied pressure will be obtained across the drain terminals of the pressure sensing MOSFETs MP2 (or MN2) and MP3 (or MN3).

ANALYTICAL MODEL OF DUAL CURRENT MIRROR BASED CMOS-MEMS INTEGRATED PRESSURE SENSOR
The proposed dual current mirror based CMOS-MEMS integrated pressure sensor consists of two square-shaped silicon diaphragms, four p-and n-channel pressure sensing MOSFETs, and CMOS dual current mirror based readout circuitry. The basic analytical models which describe the complete behaviour of the proposed sensor are as follows:

Micromechanical sensing element: Square silicon diaphragms
The proposed pressure sensing structure consists of two identical square-shaped silicon diaphragms as the pressure sensing mechanical elements. The mathematical expressions for the maximum deflection (W max ) and induced stress (σ max ) in the square diaphragm under externally applied pressure (p) are well developed [10], and are given by Equations (1) and (2).
where, 2a and h are the length and thickness of the diaphragm, and E are Poisson's ratio and Young's modulus, respectively, of diaphragm material.
Under applied pressure, maximum displacement occurs at the centre of the diaphragm, maximum positive tensile stresses are developed at the mid of the fixed edges of the diaphragm and a maximum negative compressive stress is developed at the centre of the diaphragm. Therefore, in our proposed sensor, MOS-FETs MN2 and MN3 will experience positive tensile and negative compressive stresses, respectively, developed in diaphragm-1 under applied pressure. Similarly, MOSFETs MP2 and MP3 will also experience positive tensile and negative compressive stresses, respectively, developed in diaphragm-2.

2.2
Electrical transduction mechanism: Piezo-resistive effect in MOSFET Piezoresistive effect in MOSFETs has been used as the electrical transduction technique in the proposed CMOS dual current mirror based pressure sensor. The drain-to-source current (I DS ) and channel resistance (R ch ) of a MOSFET operated in saturation region are given by the Equation (3) and (4) [37].
where, μ is the carrier mobility in channel region, C ox is the oxide capacitance per unit area, W is the channel width, L is the channel length, V GS is the gate-to-source voltage, V t is the threshold voltage, r o is the output resistance and V A is early voltage of the MOSFET. Channel resistance (R ch = r o ) of p-and n-channel MOSFET operated in saturation region can be modelled by an equivalent piezoresistors as shown in Figure 3 [33]. Furthermore in [19], it is shown that the relative change in MOSFET drain current under applied mechanical stress solely depends on stressinduced carrier mobility variation. Therefore, the relative change in carrier mobility of MOSFET under applied pressure is given by Equation (5).
where π is the piezoresistive coefficient of MOSFET and σ is the induced stress. Table 2 gives the various piezoresistive coefficients of p-and n-MOSFETs and it is observed that each of the π-coefficients of NMOS is having different magnitude with opposite sign as compared with that of PMOS. From literature [35][36], it has been found that the sign of overall piezoresistive coefficient (π) is negative for PMOS and positive for NMOS. Therefore, the effect of similar stress on the channel resistance and carrier mobility of pressure sensing NMOS and PMOS transistors will be opposite in nature, which is governed by Equation (5). Table 2 also shows the effect of stress on various MOSFETs of proposed dual current mirror pressure sensor under applied pressure.

Dual current mirror based CMOS readout circuit
A dual current mirror based CMOS readout circuit consisting of three identical p-channel MOSFETs and three identical  Unstressed condition (0) Arrows (↑) and (↓) indicate increase and decrease in the parameter value. n-channel MOSFETs as shown in Figure 1(c). On analysing the dual current mirror based pressure sensor circuit, the following expressions have been obtained: where, V DD is the supply voltage, V tn and V tp are the threshold voltages of NMOS and PMOS, V GSN1 is the gate-to-source voltage, V DSN1(/2/3) are the drain-to-source voltages, μ n1(/2/3) and μ p1(/2/3) are the electron and hole mobility of corresponding MOSFETs MN1(/2/3) and MP1(/2/3). The output voltage (V out ) proportional to externally applied input pressure is measured across the common drain terminals of pressure sensing MOSFETs MP2 and MN2, and MP3 and MN3, respectively, as shown in Figure 1(c) and is given by Equation (9).
Under zero applied pressure condition, μ p2 = μ p3 , μ n2 = μ n3 , V DSN2 = V DSN3 , the output voltage of the sensor is zero (V out = 0). Under applied pressure, there will be variations in the carrier mobility of pressure sensing MOSFETs MP2, MP3, MN2 and MN3such that μ p2 ≠ μ p3 andμ n2 ≠ μ n3 , as shown in Table 2. This will result in V DSN2 ≠V DSN3 , hence, producing in a non-zero output voltage corresponding to the input applied pressure.

SIMULATION RESULTS AND DISCUSSIONS
In this section, simulation results of dual current mirror based CMOS-MEMS integrated pressure sensor have been discussed. Finite element method (FEM) based COMSOL Multiphysics software has been used for the simulation and analysis of structural behaviour of the mechanical diaphragms and piezoresistive behaviour of pressure sensing n-and pchannel MOSFET equivalent piezoresistors embedded on the pressure sensing diaphragms. LTspice software has been utilized to evaluate electrical characteristics of dual current mirror based CMOS-MEMS integrated pressure sensor. The effect of temperature on output voltage of the sensor has also been studied. This is followed by mask layout design and step-by-step fabrication process flow of the proposed pressure sensor.

Simulation of dual current mirror based CMOS-MEMS integrated pressure sensor
The parameters used in the design and simulation of the proposed dual current mirror based pressure sensor are listed in Table 3. Simulation of the proposed pressure sensor started with the building of three dimensional pressure sensing structure consisting of diaphragms embedded with strain sensing n-and p-channel MOSFET equivalent piezoresistors using the 3D builder module of COMSOL Multiphysics software. This is followed by assigning of material properties and setting-up of proper boundary conditions for both structural analysis of pressure sensing membrane and piezoresistive behaviour of pand n-channel MOSFET equivalent piezoresistors. This was followed by meshing of pressure sensing structure as shown in Figure 4. A voltage equal to the early voltage of p-channel (and n-channel) MOSFET is applied across p-MOSFET (and n-MOSFET) equivalent piezoresistors. An input pressure in the range of 0-200 kPa with a step size of 25 kPa is then applied on the top surface of both the diaphragms in the downward direction and the solution is carried out. Figures 5, 6 show the displacement and stress profile of the pressure sensing diaphragms under an applied pressure π 11 = -66 π 11 = 1020 π 12 = 11 π 12 = -534 Pressure range 0 -200 kPa ; Step size = 25 kPa   The carrier mobilities of p-and n-channel MOSFET under no load condition are 250 cm 2 /Vs and 750 cm 2 /Vs, respectively. Figure 9 and Figure 10 show the variation in carrier mobility of p-and n-channel MOSFETs under external load condition. An enhancement of approx. 5.98 cm 2 /Vs and a reduction of approx. 0.48 cm 2 /Vs have been observed in the channel mobilty of P-MOSFETs placed at the edge and centre of the diaphragm under 200 kPa of applied pressure. An enhancement of approx. 10.71 cm 2 /Vs and a reduction of approx. 11.01 cm 2 /Vs have been observed in the channel mobility of N-MOSFETs placed at the centre and edge of the diaphragm. The variations in channel resistance and carrier mobility of p-and n-MOSFETs are governed by piezo-MOS effect given by Equation (5) and Table 2.
As depicted in Figure 1(c), a dual current mirror based CMOS circuit has been designed using standard 5 μm CMOS  Figures 11, 12 show the variation in currents and voltages at the common drain terminals of MP1 and MN1 (node-1), MP2 and MN2 (node-2), and MP3 and MN3 (node-3) as a function of applied pressure. As transistors MP1 and MN1 are embedded on the substrate and not on the diaphragm, the drain current and voltage at node-1 is independent of external pressure and remains constant. The current and voltage at node-1 are found to be approx. 842.52 μA and 4.02 V, respectively. However, the currents and voltages at node-2 and node-3 varies under applied pressure as these nodes are common drain terminals of pressure sensing transistors MP2 and MN2 embedded at the fixed edges of the diaphragms, and MP3 and MN3 embedded at the centre of the diaphragms as shown in Figure 2. A reduction of approx. 3.76 μA and an enhancement of approx. 8.26 μA in the currents at node-2 and node-3, respectively, have been observed under an applied pressure of 200 kPa. From Figure 1(a), it can be seen that MOSFETs MP2 and MN2 (also MP3 and MN3) are connected in series and can be viewed as a series combination of two MOS-FET equivalent resistors, whose resistance are calculated from Equation (4). The overall current flowing through these series connections will depend on the total sum of MOSFET equivalent series resistances. Under zero applied pressure, the series resistance of MP2 and MN2 is equal to the series resistance MP3 and MN3 and is found to be approx. 316.54 kΩ. Therefore, the currents flowing through them remain same. Under an applied pressure of 200 kPa, the series resistance of MP2 and MN2 is found to be increased to approx. 318.14 kΩ and has resulted in a reduced total current. The series resistance of MP3 and MN3 is found to be decreased to approx. 313.31 kΩ under 200 kPa of applied pressure and has resulted in an enhanced total current.
An enhancement of approx. 1080 mV and a reduction of approx. 460 mV in the voltages at node-2 and node-3, respectively, have been observed at 200 kPa pressure. These node voltages are equal to the drain-to-source voltages of MOSFETs MN2 and MN3 and changes due to the variations in the mobility of pressure sensing MOSFETs (MP2, MN2, MP3 and MN3) under applied pressure as given by Equations (7) and (8). Figure 13 shows the final output voltage of the proposed pressure sensor. From the simulation results, it is found that the full scale output voltage of the pressure sensor is approx. 1540 mV. The linearity error in the sensor output voltage is found to be less than approx. 0.1% for input pressures less than 100 kPa and approx. 0.31% at 200 kPa. The pressure sensitivity of the proposed sensor is found to be approx. 7.7 mV/kPa for an input pressure ranging from 0-200 kPa.

Mesh analysis
Mesh convergence method plays an important role in finding the accuracy of solutions obtained using numerical techniques [38][39]. In this study, the mesh convergence method was used to find out the accuracy of the simulation results of the proposed dual current mirror based pressure sensor described in Section 4.1. This method is related to how small the elements need to be, to ensure that the results of the finite element analysis are not affected substantially by reducing the size of the meshing elements. Eight different sizes of meshes (i.e. Extremely coarser, Extra coarser, Coarser, Coarse, Normal,  Fine, Finer and Extra Finer) were selected for simulating the proposed pressure sensor in COMSOL Multiphysics for an applied pressure of 200 kPa using a computer with Intel(R)-Core(TM)-i3-4010U 1.70 GHz CPU processor, 4 GB RAM and 64-bit Windows-10 operating system. The number of meshes used in first step was less than the second step and this was repeated until the eighth step. The details of the mesh analysis are given in Table 4. From the results given in Table 4, it has been observed that the changes in the solution (i.e. output voltage of the sensor) between two consecutive mesh types for Extremely Coarser to Extra Coarser is found to be approx. 9 %, Extra Coarser to Coarser is found to be approx. 4.7 %, from Coarser to Extra finer are found to be less than approx. 0.5 % only. Figure 14 shows the plot of output voltage of the sensor as a function of number of mesh elements. It has been observed that the output voltage saturates after approx. 6292 elements. The results can be considered as converged for any mesh type from Coarser (6292 elements) to Extra finer (59521 elements). Therefore, the results described in Section 4.1 were obtained using Normal mesh (14470 elements) and they fall within the range of

3.3
Effect of temperature on the output voltage and sensitivity of pressure sensor Current mirrors are most commonly used as constant-current sources for biasing of integrated circuits (ICs) [37]. A current mirror generates a constant reference current at the input side of the mirror circuit and replicates the reference current in its output transistors. One of the main advantages of current mirror is that the currents of transistors at input and output side of the current mirror track each other in case of changes in operating temperature and have low temperature sensitivity [37,[40][41]. Using this concept, the temperature compensation behaviour of our proposed dual current mirror based pressure sensor can be described. Considering the proposed pressure sensor consists of ideal and identical p-and n-channel MOS-FETs. Under zero applied pressure, any change in operating temperature will result in similar variations in the electrical characteristics of all PMOS transistors (MP1, MP2 and MP3) and similar variations in electrical characteristics of all NMOS transistors (MN1, MN2 and MN3). This will result in equal voltages across the common drain terminals of MP1 & MN1 (node-1), MP2 & MN2 (node-2), and MP3 & MN3 (node-3), and therefore, result in zero output voltage (i.e., V out = V DSN2 − V DSN3 = 0). However, under externally applied pressure, the proposed dual current mirror based pressure sensor will produce an output voltage proportional to the input applied pressure only, irrespective of any variation in the temperature.
The effect of temperature on the output voltage of the pressure sensor is also studied using LTspice software for an operating temperature ranging from −50 to 100 • C. Figure 15 shows the plot of sensor output voltage as a function of applied pressure at different temperatures ranging from 50 to 100 • C. Figure 16 shows the plot of sensor output voltage as a function of temperature at different pressures ranging from 0 to 200 kPa. From the simulation results, it has been observed that the sensor output voltage decreases with increase in temperature. The pressure sensitivity of the sensor reduces with temperature and is found to be approx. 7.73, 7.71, 7.69 and 7.57 mV/kPa at  operating temperatures of −50, 0, 50 and 100 • C, respectively. It has also been observed that the temperature sensitivity of the sensor increases with applied pressure and is found to be approx. −0.005, −0.010, −0.015 and −0.213 mV/ • C for an input applied pressure of 50, 100, 150 and 200 kPa, respectively. A maximum change of approx. 2.07% in the output voltage of the pressure sensor has been observed for the given temperature range at 200 kPa of applied pressure. These results show that the proposed dual current mirror integrated pressure sensor has low temperature sensitivity. This variation in the output voltage due to temperature change is because the hole and electron mobilities of p-and n-MOSFETs are different under applied pressure (μ p1 ≠ μ p2 ≠ μ p3 and μ n1 ≠ μ n2 ≠ μ n3 ) and decrease with increase in temperature above −50 • C [42] The decrease in the output voltage with increase in temperature is governed by Equations (5), (7)(8)(9). Table 5 shows a comparison of temperature sensitivity of dual current mirror integrated pressure sensor with recently reported related works on CMOS

MASK LAYOUT DESIGN AND FABRICATION PROCESS FLOW
The mask layout of the proposed dual current mirror CMOS-MEMS integrated pressure sensor chip of size 0.8 mm × 0.8 mm has been designed using L-Edit software. Figure 17 depicts an eight level mask layout design that has been used for the fabrication of proposed pressure sensor employing "CMOS first" and "MEMS last" technique.
A step-by-step fabrication process flow has been proposed for the development of CMOS dual current mirror based integrated pressure sensor. The fabrication starts with chemically cleaned boron-doped p-type (100), double side polished silicon wafer as shown in Figure 18(a). Then, a field oxide of 1 μm thick is thermally grown on both sides of the wafer using thermal oxidation technique at 1100 • C. This is followed by defining regions for creating n-well using thermal diffusion process. In the next step, complete oxide is etched out from the front side of the substrate using buffered oxide etchant (BOE) solution. A thin gate-oxide of 85 nm thick is thermally grown using dry oxidation process at 1100 • C. A polysilicon layer of 0.3 μm is deposited using standard low pressure chemical vapour deposition (LPCVD) process at 620 • C. This is followed by the defining of polysilicon gate, creating regions for n+ source and drain regions in order to form n-channel MOSFETs. Phosphorus doping is carried out at 1000 • C using thermal diffusion process to create n+ source and drain regions for n-channel MOSFET. During thermal diffusion of phosphorus, a thin layer of phosphosilicate is formed over the entire wafer surface. In the next step, regions for making p+ source and drain regions are defined. Boron doping at 1000 • C is carried out using ther-FIGURE 18 (a) Chemically cleaned initial p-type (100) silicon substrate, (b) dual current mirror pressure sensing CMOS circuit covered with metal layer, (c) bulk micromachining of silicon from the backside of the wafer for realizing diaphragm, and (d) dual current mirror integrated pressure sensor after fabrication mal diffusion process for making p+ source and drain in order to form p-channel MOSFET. Similarly, a thin layer of borosilicate layer covers the entire surface of wafer. This is followed by patterning and defining regions for making vias for metal contacts from source, drain and gate regions of n-and p-channel MOSFETs. In the next step, deposition of aluminium is carried out using sputtering for making contact from source, drain and gate regions. Figure 18(b) shows the fabrication of proposed dual current mirror pressure sensing CMOS circuit covered with aluminium metal layer. This is followed by pattering and defining of backside window for making cavity and realizing pressure sensing silicon diaphragm using bulk micromachining of silicon from the backside of the wafer as shown in Figure 18(c). Finally, in the next step, patterning and defining aluminium metal is carried out for making connecting lines and contact pads as shown in Figure 18(d). This completes the fabrication of the proposed dual current mirror integrated pressure sensor.

CONCLUSION
In this article, a detailed study on design and implementation of a dual current mirror based CMOS circuit for the design and development of highly sensitive CMOS-MEMS integrated pressure sensor has been presented. This dual current mirror based pressure sensor design is new and novel which is compatible to standard CMOS technology. Simulation results of the proposed pressure sensor show that the proposed sensor has a full scale output voltage of approx. 1540 mV for an input applied pressure of 200 kPa with a pressure sensitivity of approx. 7.7 mV/kPa which is significantly higher than recently reported MOSFET based pressure sensors. A marginal change of approx. 2.07% in the output voltage of proposed CMOS dual current mirror based integrated pressure sensor has been observed for an operating temperature ranging from −50 to 100 • C. The mask layout has been designed and a step-by-step fabrication process flow has been proposed for the development of CMOS dual current mirror based integrated pressure sensor. This proposed dual current mirror based CMOS circuit has a promising application in field of CMOS-MEMS integrated pressure sensors and may be an alternative to the traditional Wheatstone bridge based readout circuits.